Approaches to Quantum Gravity

More documents

Recommendations

Info

Contents List of contributors Preface page x xv Part I Fundamental ideas and general formalisms 1 1 Unfinished revolution 3 C. Rovelli 2 The fundamental nature of space and time 13 G. ’t Hooft 3 Does locality fail at intermediate length scales? 26 R. D. Sorkin 4 Prolegomena to any future Quantum Gravity 44 J. Stachel 5 Spacetime symmetries in histories canonical gravity 68 N. Savvidou 6 Categorical geometry and the mathematical foundations of Quantum Gravity 84 L. Crane 7 Emergent relativity 99 O. Dreyer 8 Asymptotic safety 111 R. Percacci 9 New directions in background independent Quantum Gravity 129 F. Markopoulou Questions and answers 150 Part II String/M-theory 167 10 Gauge/gravity duality 169 G. Horowitz and J. Polchinski vii
Page 2: This page intentionally left blank
Page 8: APPROACHES TO QUANTUM GRAVITY Towar
Page 12: A Sandra
Page 20: Contents ix 25 Doubly special relat
Page 24: List of contributors xi O. Dreyer T
Page 28: List of contributors xiii W. Taylor
Page 34: xvi Preface new mathematics as well
Page 38: xviii Preface as the current tentat
Page 44: Part I Fundamental ideas and genera
Page 50: 4 C. Rovelli QFT relies heavily on
Page 54: 6 C. Rovelli For instance, the Heis
Page 58: 8 C. Rovelli Conceptually, the key
Page 62: 10 C. Rovelli In addition, a number
Page 66:
12 C. Rovelli [20] S. W. Hawking,
Page 70:
14 G. ’t Hooft of time, of Cauchy
Page 74:
16 G. ’t Hooft generally, in 2 +
Page 78:
18 G. ’t Hooft of the small-dista
Page 82:
20 G. ’t Hooft that a theory exis
Page 86:
22 G. ’t Hooft This means that th
Page 90:
24 G. ’t Hooft 2.7 Gauge- and dif
Page 94:
3 Does locality fail at intermediat
Page 98:
28 R. D. Sorkin a little thought in
Page 102:
30 R. D. Sorkin this approach one n
Page 106:
32 R. D. Sorkin The suggestion of o
Page 110:
34 R. D. Sorkin But is our “discr
Page 114:
36 R. D. Sorkin (as one might have
Page 118:
38 R. D. Sorkin It seems likely tha
Page 122:
40 R. D. Sorkin in particular, woul
Page 126:
42 R. D. Sorkin small, as discussed
Page 130:
4 Prolegomena to any future Quantum
Page 134:
46 J. Stachel breakups, it is impor
Page 138:
48 J. Stachel gauge fields and GR,
Page 142:
50 J. Stachel where S is any 2-surf
Page 146:
52 J. Stachel connection (see, e.g.
Page 150:
54 J. Stachel of a projective struc
Page 154:
56 J. Stachel problem on a spacelik
Page 158:
58 J. Stachel (3) a break-up of the
Page 162:
60 J. Stachel simplification of the
Page 166:
62 J. Stachel investigate (3 + 1) a
Page 170:
64 J. Stachel partitioned into slic
Page 174:
66 J. Stachel [13] S. Frittelli, C.
Page 178:
5 Spacetime symmetries in histories
Page 182:
70 N. Savvidou of time. The develop
Page 186:
72 N. Savvidou In order to define c
Page 190:
74 N. Savvidou The novel feature in
Page 194:
76 N. Savvidou We start instead fro
Page 198:
78 N. Savvidou Relation between the
Page 202:
80 N. Savvidou 5.4 A spacetime appr
Page 206:
82 N. Savvidou the T 0 variables -
Page 210:
Categorical geometry and the mathem
Page 214:
86 L. Crane called morphisms [1]. A
Page 218:
88 L. Crane are defined combinatori
Page 222:
90 L. Crane 6.3.1 The BC categorica
Page 226:
92 L. Crane Classical behavior occu
Page 230:
94 L. Crane One could then apply th
Page 234:
96 L. Crane This model also has a n
Page 238:
98 L. Crane [13] J. Barrett and L.
Page 242:
100 O. Dreyer Is spacetime fundamen
Page 246:
102 O. Dreyer Since the inverse pro
Page 250:
104 O. Dreyer where we have denoted
Page 254:
106 O. Dreyer and the points are th
Page 258:
108 O. Dreyer m 1 m 2 =− v 2 v 1
Page 262:
110 O. Dreyer In addition to the pr
Page 266:
112 R. Percacci In section 8.2 I in
Page 270:
114 R. Percacci this case the theor
Page 274:
116 R. Percacci The requirement of
Page 278:
118 R. Percacci be bounded. This is
Page 282:
120 R. Percacci where the heat kern
Page 286:
122 R. Percacci ~ G 1 0.8 0.6 0.4 0
Page 290:
124 R. Percacci will still be possi
Page 294:
126 R. Percacci Einstein-Hilbert ac
Page 298:
128 R. Percacci [24] O. Lauscher an
Page 302:
130 F. Markopoulou has been claimed
Page 306:
132 F. Markopoulou vertex x ∈ V (
Page 310:
134 F. Markopoulou Note that comple
Page 314:
136 F. Markopoulou 9.2.2 The meanin
Page 318:
138 F. Markopoulou Fock space for t
Page 322:
140 F. Markopoulou A = 1 A 2 A 3 A
Page 326:
142 F. Markopoulou effective theori
Page 330:
144 F. Markopoulou Quantum Field Th
Page 334:
146 F. Markopoulou is concerned wit
Page 338:
148 F. Markopoulou The dynamics is
Page 342:
Questions and answers • Q - L. Cr
Page 346:
152 Questions and answers Hausdorff
Page 350:
154 Questions and answers - A-R.Sor
Page 354:
156 Questions and answers Now a goo
Page 358:
158 Questions and answers would see
Page 362:
160 Questions and answers 3. You me
Page 366:
162 Questions and answers - A - R.
Page 370:
164 Questions and answers notion of
Page 376:
Part II String/M-theory
Page 382:
170 G. Horowitz and J. Polchinski a
Page 386:
172 G. Horowitz and J. Polchinski w
Page 390:
Page 394:
Page 398:
178 G. Horowitz and J. Polchinski T
Page 402:
180 G. Horowitz and J. Polchinski m
Page 406:
182 G. Horowitz and J. Polchinski N
Page 410:
184 G. Horowitz and J. Polchinski c
Page 414:
186 G. Horowitz and J. Polchinski [
Page 418:
188 T. Banks This looks peculiar to
Page 422:
190 T. Banks This lightning review
Page 426:
192 T. Banks Since the holographic
Page 430:
194 T. Banks definition of local ev
Page 434:
196 T. Banks we have postulated are
Page 438:
198 T. Banks with observerphilic de
Page 442:
200 T. Banks de Sitter horizon is t
Page 446:
202 T. Banks of the dS-Schwarzschil
Page 450:
204 T. Banks Thus, there are of ord
Page 454:
206 T. Banks it has given us a cons
Page 458:
208 T. Banks [3] G. T. Horowitz, Th
Page 462:
12 String field theory W. TAYLOR 12
Page 466:
212 W. Taylor possible configuratio
Page 470:
214 W. Taylor raising operators α
Page 474:
216 W. Taylor ❍❨ 1 ❍❍✟
Page 478:
218 W. Taylor level truncation is t
Page 482:
220 W. Taylor different description
Page 486:
222 W. Taylor In closed string fiel
Page 490:
224 W. Taylor closed string field t
Page 494:
226 W. Taylor or other 6D manifold.
Page 498:
228 W. Taylor [37] W. Taylor, & B.
Page 502:
230 Questions and answers 3. You st
Page 506:
232 Questions and answers (proving
Page 512:
13 Loop quantum gravity T. THIEMANN
Page 516:
Loop quantum gravity 237 13.2 Canon
Page 520:
Loop quantum gravity 239 In what fo
Page 524:
Loop quantum gravity 241 equivalenc
Page 528:
Loop quantum gravity 243 ∂ F τ f
Page 532:
Loop quantum gravity 245 will play
Page 536:
Loop quantum gravity 247 U(ϕ)T n =
Page 540:
Loop quantum gravity 249 a definite
Page 544:
Loop quantum gravity 251 [28] T. Th
Page 548:
14 Covariant loop quantum gravity?
Page 552:
Covariant loop quantum gravity? 255
Page 556:
Page 560:
Page 564:
Page 568:
Page 572:
Page 576:
Page 580:
Page 584:
Page 588:
The spin foam representation of loo
Page 592:
Page 596:
Page 600:
Page 604:
Page 608:
Page 612:
Page 616:
Page 620:
Page 624:
Three-dimensional spin foam Quantum
Page 628:
Page 632:
Page 636:
Page 640:
Page 644:
Page 648:
Page 652:
Page 656:
Page 660:
Page 664:
The group field theory approach to
Page 668:
Page 672:
Page 676:
Page 680:
Page 684:
Page 688:
Page 692:
Page 696:
Page 700:
Page 704:
Page 708:
Questions and answers 333 the holes
Page 712:
Questions and answers 335 their vac
Page 716:
Questions and answers 337 of some s
Page 724:
18 Quantum Gravity: the art of buil
Page 728:
Quantum Gravity: the art of buildin
Page 732:
Page 736:
Page 740:
Page 744:
Page 748:
Page 752:
Page 756:
Page 760:
Page 764:
Quantum Regge calculus 361 is given
Page 768:
Quantum Regge calculus 363 group. W
Page 772:
Quantum Regge calculus 365 emanatin
Page 776:
Quantum Regge calculus 367 We will
Page 780:
Quantum Regge calculus 369 reason,
Page 784:
Quantum Regge calculus 371 gravitat
Page 788:
Quantum Regge calculus 373 where ξ
Page 792:
Quantum Regge calculus 375 [4] J. W
Page 796:
Quantum Regge calculus 377 [52] M.
Page 800:
Consistent discretizations as a roa
Page 804:
Page 808:
Page 812:
Page 816:
Page 820:
Page 824:
Page 828:
21 The causal set approach to Quant
Page 832:
The causal set approach to Quantum
Page 836:
Page 840:
Page 844:
Page 848:
Page 852:
Page 856:
Page 860:
Page 864:
Page 868:
Page 872:
Page 876:
Page 880:
Page 884:
Page 888:
Page 896:
22 Quantum Gravity phenomenology G.
Page 900:
Quantum Gravity phenomenology 429 T
Page 904:
Quantum Gravity phenomenology 431 t
Page 908:
Quantum Gravity phenomenology 433 c
Page 912:
Quantum Gravity phenomenology 435 p
Page 916:
Quantum Gravity phenomenology 437 F
Page 920:
Quantum Gravity phenomenology 439 l
Page 924:
Quantum Gravity phenomenology 441 p
Page 928:
Quantum Gravity phenomenology 443 w
Page 932:
Quantum Gravity phenomenology 445 i
Page 936:
Quantum Gravity phenomenology 447 s
Page 940:
Quantum Gravity phenomenology 449 [
Page 944:
Quantum Gravity and precision tests
Page 948:
Page 952:
Page 956:
Page 960:
Page 964:
Page 968:
Page 972:
Page 976:
Algebraic approach to Quantum Gravi
Page 980:
Page 984:
Page 988:
Page 992:
Page 996:
Page 1000:
Page 1004:
Page 1008:
Page 1012:
Page 1016:
Page 1020:
Page 1024:
Page 1028:
25 Doubly special relativity J. KOW
Page 1032:
Doubly special relativity 495 DSR t
Page 1036:
Doubly special relativity 497 On th
Page 1040:
Doubly special relativity 499 some
Page 1044:
Doubly special relativity 501 [x 0
Page 1048:
Doubly special relativity 503 that
Page 1052:
Doubly special relativity 505 can b
Page 1056:
Doubly special relativity 507 scale
Page 1060:
26 From quantum reference frames to
Page 1064:
From quantum reference frames to de
Page 1068:
Page 1072:
Page 1076:
Page 1080:
Page 1084:
Page 1088:
Page 1092:
Page 1096:
Page 1100:
Lorentz invariance violation & its
Page 1104:
Page 1108:
Page 1112:
Page 1116:
Page 1120:
Page 1124:
Page 1128:
Page 1132:
Page 1136:
Page 1140:
Generic predictions of quantum theo
Page 1144:
Page 1148:
Page 1152:
Page 1156:
Page 1160:
Page 1164:
Page 1168:
Page 1172:
Page 1176:
Page 1180:
Page 1184:
Questions and answers • Q - L. Cr
Page 1188:
Questions and answers 573 frame. Ju
Page 1192:
Questions and answers 575 - A - J.
Page 1196:
Questions and answers 577 where thi
Page 1200:
Questions and answers 579 would all
Page 1204:
Index 581 cosmology, 26, 155, 184,
Page 1208:
Index 583 emergent, 99, 109, 163, 1
show all

Approaches to Quantum Gravity

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?